On Variograms in Point Process Statistics,II: Models of Markings and Ecological Interpretation

This paper presents new models for marked point processes for describing forestry data. In these models two factors play a role: Long‐range variability is modeled by a random field, which may describe environmental variability, while short‐range variability is caused by the interaction of points of two classes. These models may help in the interpretation of empirical mark variograms as is shown by two examples from forestry statistics.     

地质统计学在昆虫种群空间结构研究中的应用概述

地质统计学是用来人间相关变量结构的统计学方法,地质统计学中的变差函数和变差图,可分析空间变量在不同方向或不同环境条件下的空间结构。     

Tests for independence between marks and points of a marked point process

A convenient assumption while modeling a marked point process is that the observations (i.e., marks) and the locations (i.e., points) are independent. We propose new graphical and formal testing approaches to test for this assumption. The proposed graphical procedures are easy to obtain and can be used to diagnose the nature and range of dependence between marks and points. The formal testing procedures require only minimal conditions on marks and thus can be applied to a variety of settings. We illustrate these procedures through a simulation study and an application to some real data.     

Modelling pairwise dependence of maxima in space

We model pairwise dependence of temporal maxima, such as annualmaxima of precipitation, that have been recorded in space, eitheron a regular grid or at irregularly spaced locations. The constructionof our estimators stems from the variogram concept. The asymptoticproperties of our pairwise dependence estimators are establishedthrough properties of empirical processes. The performance ofour approach is illustrated by simulations and by the treatmentof a real dataset. In addition to bringing new results aboutthe asymptotic behaviour of copula estimators, the latter beinglinked to first-order variograms, one main advantage of ourapproach is to propose a simple connection between extreme valuetheory and geostatistics.     

Identifying spatial relationships at multiple scales: principal coordinates of neighbour matrices (PCNM) and geostatistical approaches

We compared two methodological approaches – principal coordinate analysis of neighbour matrices (PCNM) and geostatistics – that both aim at extracting several spatial scales in order to identify spatial relationships between organisms and environmental variables at multiple scales. From a statistical point of view, PCNM analysis and geostatistics come from "two different worlds"– PCNM is based on classical "data analysis" while geostatistical modelling is developed in a probabilistic context. These two methods were used to investigate the spatial relationships between defoliation caused by spruce budworm Choristoneura fumiferana and bioclimatic conditions in Ontario since 1941 through a wide range of scales. On the one hand, PCNM variables related to defoliation frequency were partitioned into four spatial submodels representing respectively four spatial scales: very broad scale (ca>300 km), broad scale (ca 180 km), fine (ca 100 km), and very fine (<80 km). On the other hand, nested variogram modelling was used to identify the relevant scales. The nested variogram model was composed of four variograms with different characteristic scales close to those of the PCNM spatial submodels. Maps of PCNM submodels and kriging components revealed similar spatial patterns of defoliation frequency at very broad and broad scales while spatial patterns at fine and very fine scales looked quite different. Both methods showed that defoliation by spruce budworm occurs at the broader spatial scales but may be explained by fluctuations at the smaller scales. Finally, results based on geostatistics using a Linear Model of Coregionalisation suggested that climatic conditions can be considered to act at the level of outbreak dynamics while the tree community of spruce budworm's principal hosts controls local population dynamics.     

Illustrations and guidelines for selecting statistical methods for quantifying spatial pattern in ecological data

This paper aims to provide guidance to ecologists with limited experience in spatial analysis to help in their choice of techniques. It uses examples to compare methods of spatial analysis for ecological field data. A taxonomy of different data types is presented, including point‐ and area‐referenced data, with and without attributes. Spatially and non‐spatially explicit data are distinguished. The effects of sampling and other transformations that convert one data type to another are discussed; the possible loss of spatial information is considered.
Techniques for analyzing spatial pattern, developed in plant ecology, animal ecology, landscape ecology, geostatistics and applied statistics are reviewed briefly and their overlap in methodology and philosophy noted. The techniques are categorized according to their output and the inferences that may be drawn from them, in a discursive style without formulae. Methods are compared for four case studies with field data covering a range of types. These are: 1) percentage cover of three shrubs along a line transect; 2) locations and volume of a desert plant in a 1 ha area; 3) a remotely‐sensed spectral index and elevation from 10⁵ km² of a mountainous region; and 4) land cover from three rangeland types within 800 km² of a coastal region. Initial approaches utilize mapping, frequency distributions and variance‐mean indices. Analysis techniques we compare include: local quadrat variance, block quadrat variance, correlograms, variograms, angular correlation, directional variograms, wavelets, SADIE, nearest neighbour methods, Ripley's (t), and various landscape ecology metrics.
Our advice to ecologists is to use simple visualization techniques for initial analysis, and subsequently to select methods that are appropriate for the data type and that answer their specific questions of interest. It is usually prudent to employ several different techniques.     

The Autocovariance Function for Marked Point Processes: A Comparison between Two Different Approaches

Exploratory analysis of marked point patterns has previously been conducted using two disjoint techniques, namely the mark correlation function and spectral analysis. Our purpose here is to present two alternative autocovariance estimators to the mark correlation function which not only apply in both planar and lattice situations, but which in the lattice case can also be considered in terms of the inverse Fourier transform of the spectrum. Moreover, they can be applied to isotropic or anisotropic marked point patterns. Various examples are presented to show how these estimators perform when applied to data sets possessing different kinds of mark structure, and a rank test procedure is proposed to enable the construction of empirical tests of hypothesis.     

Parameter estimation and model selection for Neyman-Scott point processes

This paper proposes an approximative method for maximum likelihood estimation of parameters of Neyman-Scott and similar point processes. It is based on the point pattern resulting from forming all difference points of pairs of points in the window of observation. The intensity function of this constructed point process can be expressed in terms of second-order characteristics of the original process. This opens the way to parameter estimation, if the difference pattern is treated as a non-homogeneous Poisson process. The computational feasibility and accuracy of this approach is examined by means of simulated data. Furthermore, the method is applied to two biological data sets. For these data, various cluster process models are considered and compared with respect to their goodness-of-fit.     

Characterizing the spatial structures of riparian plant communities in the lower reaches of the Heihe River in China using geostatistical techniques

Geostatistical techniques are used to evaluate spatial characteristics of riparian plant communities that were mapped within a portion of the lower reaches of the Heihe River. The spatial structures of different plant communities were characterized using nugget, range and sill parameters of spherical or exponential model variograms. Model variograms revealed different plant communities with distinctive spatial properties that were quantified effectively by the parameters used in these models. Model variograms were fit to experimental variograms calculated from diameter at breast height and plant cover data collected for three 2,000 m × 5 m, nine 500 m × 5 m, and three 200 m × 2 m transects. The 2,000 m × 5 m transects were oriented perpendicular to the river and the other transects were located in such a way as to sample communities dominated by different plants. Riparian plant communities in the lower reaches of the Heihe River show patterns of patchiness, and the plant communities are mainly dominated by mature Populus euphratica, young P. euphratica, Tamarix chinensis, and Sophora alopecuroides. The maximum model variogram range for all communities was 55 m, suggesting that transects must be at least this long in order to be able to classify them unambiguously into recognizable communities. Experimental variograms were calculated for all plants in each of four mapped plant communities. The results show that the T. chinensis and S. alopecuroides dominated plant communities have distinctively large ranges, and the spatial structures of P. euphratica dominated plant communities show multiscale change. In the 2,000 m × 5 m transects, the spatial structures of riparian plant communities show a distinct change at the scale of 430 m, because this scale also is the scale of vegetation patchiness turnover, and at scales of more than 430 m the spatial structure of the community increases significantly. These findings confirm the potential of using high-resolution remote sensing data and geostatistics for determining the vegetation community structures of riparian plant communities.     

A Computer Programme Package for the Statistical Analysis of Spatial Point Processes in a Square

A computer programme for the statistical analysis of point data in a square is described. Several tests for randomness of the distribution of points are possible. The most comprehensive of these are comparisons of the empirical distributions of the inter-point and closest neighbour distances with their respective expected distributions under complete randomness, and tests based on Ripley' L function; using these, significant aggregation or regularity can be identified. It is also possible to calculate statistics of properties (“attributes”) associated with each spatial point, as well as to compare statistics for sub-areas of the experimental square. Several measures of spatial autocorrelation are available, amongst them correlograms and variograms. The programme can also find the tesselation of the study area and correlate tile properties with the point attributes. The procedures are illustrated by references to the spatial distribution and mound heights of Trinevitermes trinervoides on a study area in South Africa. Although the programme was developed specifically for application in entomology, it could be used to analyse data from many other disciplines.     

Kriging with nonparametric variance function estimation

A method for fitting regression models to data that exhibit spatial correlation and heteroskedasticity is proposed. It is well known that ignoring a nonconstant variance does not bias least-squares estimates of regression parameters; thus, data analysts are easily lead to the false belief that moderate heteroskedasticity can generally be ignored. Unfortunately, ignoring nonconstant variance when fitting variograms can seriously bias estimated correlation functions. By modeling heteroskedasticity and standardizing by estimated standard deviations, our approach eliminates this bias in the correlations. A combination of parametric and nonparametric regression techniques is used to iteratively estimate the various components of the model. The approach is demonstrated on a large data set of predicted nitrogen runoff from agricultural lands in the Midwest and Northern Plains regions of the U.S.A. For this data set, the model comprises three main components: (1) the mean function, which includes farming practice variables, local soil and climate characteristics, and the nitrogen application treatment, is assumed to be linear in the parameters and is fitted by generalized least squares; (2) the variance function, which contains a local and a spatial component whose shapes are left unspecified, is estimated by local linear regression; and (3) the spatial correlation function is estimated by fitting a parametric variogram model to the standardized residuals, with the standardization adjusting the variogram for the presence of heteroskedasticity. The fitting of these three components is iterated until convergence. The model provides an improved fit to the data compared with a previous model that ignored the heteroskedasticity and the spatial correlation.     

南极半岛北部南极磷虾渔业空间点格局特征

南极磷虾作为南极生态系统中的关键物种,在空间分布上常表现出集群特征.这也反映到磷虾渔业生产的空间格局特征上.为了探讨捕捞能力有明显差异的船队在高/低单位捕捞努力量渔获量(CPUE)的情况下空间点分布格局特征及其生态学效应,基于南极半岛北部海域的两艘中国南极磷虾渔船(船A为专业南极磷虾渔船,船B为在智利竹筴鱼渔场与南极磷虾渔场转换的兼作渔船)的磷虾渔业数据,从空间点格局的角度出发,分别从两船的高、低CPUE的空间点格局在不同尺度上聚集特征,高、低CPUE在不同尺度上的二元点格局相关关系,以及CPUE点标记格局下的相关性关系等3个方面进行了分析.Ripley的L函数和标记相关函数分析结果表明: 研究对象在空间窗口所有尺度上的空间格局均表现为聚集性,高、低CPUE下均有聚集发生;在15 km尺度上,聚集强度近最大,在15~50 km尺度下,聚集程度稳定;总体上点格局分布的聚集强度依次为:船A高CPUE>船B低CPUE>船B高CPUE>船A低CPUE.船A高、低CPUE在0~75 km尺度上为正相关关系,在大于75 km尺度上为随机关系;船B在所有尺度上的高、低CPUE均为正相关,说明了低CPUE点事件伴随高CPUE的点事件同步发生,两者在大部分尺度下均显著相关.这是磷虾集群模式的动态性和复杂性造成.船A各点的CPUE值在0~44 km尺度上呈正相关,在44~80 km尺度上呈负相关;船B各点的CPUE值在50~70 km尺度上呈负相关,在其他尺度上无显著相关性;正相关反映了磷虾密集集群的种群分布特性,而负相关表明了磷虾群间由于食物和空间原因存在一定的竞争关系.捕捞能力强的船A和捕捞能力较弱的船B在点格局分布上存在较大差异.专业南极磷虾渔船更适于开展磷虾作业空间点格局分析及相关科学调查工作.     

Correlations in one-dimensional fully developed chaos

Correlations in the baker map and the tent map as examples of one-dimensional, fully developed chaos are considered. It is shown, utilizing symbolic dynamical systems derived from these maps, that the vanishing second-order correlation function is not sufficient to guarantee uncorrelatedness. Importance of the higher-order, especially third-order, correlation functions is emphasized for chaotic systems. In search of the quantities that grasp correlational behaviors as a whole in chaotic systems, it is proposed to use the fixed-separation correlation integral, which is a modified quantity of the usual correlation integral devised to calculate the fractal dimension of strange attractors, for these maps. It is shown that the new quantity contains all the even-number orders of autocorrelation function that are commonly considered.     

大兴安岭次生林区优势种落叶松分布格局及竞争作用

竞争是形成特定群落结构、构成分布格局的基本驱动力之一,树种的空间分布和大小并不是相互独立的,而是广泛受到竞争过程影响。在大兴安岭设置一块具有代表性的天然次生林恢复样地,采用点格局分析中的最近邻体距离G（r）函数、双关联函数g（r）和基于个体胸径标记的点格局分析方法同时结合4种点格局零模型（完全随机模型、均值托马斯模型、随机标签模型、先决条件零模型）研究分析大兴安岭次生林区优势种落叶松不同生活史阶段的分布格局、关联性及竞争作用。研究结果显示：落叶松不同发育阶段分布格局不同、同一发育阶段不同研究尺度分布格局也不同;落叶松种群内存在潜在的竞争、且竞争作用与龄级和研究尺度有关;落叶松幼龄个体在小尺度（r<5m）下的聚集分布是由扩散限制作用和竞争作用所导致;落叶松种群内成龄与幼龄个体间有较强的正关联性、成龄个体对幼龄个体在小尺度下有明显的庇护作用;标记点格局分析方法在检测植物群落中的竞争作用时敏感性较高。     

Spatial Analysis of Twaite Shad,Alosa fallax (Lacepède, 1803), in the Southern North Sea: Application of Non‐Linear Geostatistics as a Tool to Search for Special Areas of Conservation

This study aims to evaluate the suitability of non‐linear geostatistics and indicator kriging (IK) as a tool in environmental impact assessment and nature conservation, in particular to search for potential Special Areas of Conservation (SAC) for the endangered fish species twaite shad, Alosa fallax (Lacepède , 1803) within the German Exclusive Economical Zone (EEZ) of the North Sea. To analyse the spatial distribution of this fish species, data on standardised biomass index (catch per unit effort, c.p.u.e., kg × 30 min^–1) from 1996 to 2001 were used, regarding the third and fourth quarters of each year, respectively. Thereby we assume that the spatial distribution can be described as a time‐invariant process. This assumption is supported by information on annual sampling effort, allocation of hauls and spatial distribution of the positive catches. All indicator variograms obtained for different c.p.u.e. cut‐off values displayed distinct spatial structures, clearly indicating that the indicator variables were spatially autocorrelated. Gaussian models were fitted by least‐squares methods and were evaluated with a goodness‐of‐fit statistic. Subsequently, IK was employed to estimate the probability of exceeding the c.p.u.e. cut‐off values for the twaite shad in the investigation area. These were highest in the Weser‐ and Elbe‐estuary, probably because of migrations of twaite shad to and from estuaries at the time of investigation due to spawning, while within the German EEZ of the North Sea no such areas with increased probabilities could be discerned. Thus, although available data did not allow to identify and implement any SAC in the German EEZ, the methods employed here can be regarded as a promising management tool in biological conservation issues. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Collective motions in proteins investigated by X-ray diffuse scattering

We have developed theoretical models for analysis of X-ray diffuse scattering from protein crystals. A series of models are proposed to be used for experimental data with different degrees of precision. First, we propose the normal mode model, where conformational dynamics of a protein is assumed to occur mostly in a limited conformational subspace spanned by a small number of low-frequency normal modes in the protein. When high precision data are available, variances and covariances of the normal mode variables can be determined from experimental data using this model. For experimental data with lower degrees of precision, we introduce a series of simpler models. These models express the covariance matrix using relatively simple empirical correlation functions by assuming the correlation between a pair of atoms to be isotropic. As an application of these simpler models, we calculate diffuse-scattering patterns from a human lysozyme crystal to examine how each adjustable parameter in the models affects general features of the resulting patterns. The results of the calculation are summarized as follows. (1) The higher order scattering makes a significant contribution at high resolutions. (2) The resulting simulated patterns are sensitive to changes in correlation lengths of about 1 Å, as well as to changes of the functional form of the correlation function. (3) But only the “average” value of the intra- and intermolecular correlation lengths seems to determine the gross features of the pattern. (4) The effect of the atom-dependent amplitude of fluctuations is difficult to observe. © 1994 John Wiley & Sons, Inc.     

Combining stratification and up-scaling method-block cokriging with remote sensing imagery for sampling and mapping an erosion cover factor

When a ground and vegetation cover factor related to soil erosion is mapped with the aid of remotely sensed data, a cost-efficient sample design to collect ground data and to obtain an accurate map is required. However, the supports used to collect ground data are often smaller than the desirable pixels used for mapping, which leads to complexity in developing procedures for sample design and mapping. For these purposes, a sampling and mapping method was developed by integrating stratification and an up-scaling method in geostatistics — block cokriging with Landsat Thematic Mapper imagery. This method is based on spatial correlation and stratified sampling. It scales up not only the ground sample data but also the uncertainties associated with the data aggregation from smaller supports to larger pixels or blocks. This method uses the advantages of both stratification and block cokriging variance-based sample design, which leads to sample designs with variable grid spacing, and thus significantly increases the unit cost-efficiency of sample data in sampling and mapping. This outcome was verified by the results of this study.     

我国栗属物种(Castanea millissima)地理分布及其空间特征分析

在广泛收集我国栗属3个物种板栗(C.mollissimaBl.)、茅栗(C.seguinii)和锥栗(C.Henryi(skan)Rehd.etWils.)地理分布资料的基础上,利用地统计学方法对它们的上限和下限的分布幅度进行了分析,给出了分布高度的插值结果,并对其估值结果进行了分析。结果表明,板栗和茅栗的分布上限和下限呈现出由东向西逐渐升高的趋势。而且越向西其变化趋势越为明显;锥栗则表现出由东南向西北逐渐升高的趋势,其变化幅度也相对较小。对3种植物分布高度插值结果进行的误差分析表明茅栗和锥栗的估测值和实际值非常吻合,茅栗误差较小,大都在4%以下锥栗误差在6%以下;而板栗由于多为人工栽培,受人为因素影响大,因此,其估测值的误差相对较大,在0～20%之间波动,但其大部分误差也都小于10%。这些结果说明,地统计学方法能够良好地拟合自然条件下物种的地理分布规律,而人为因素影响强烈下的物种由于其分布的规律性受到破坏而影响了预测效果。     

自噬对血管功能的影响及与相关疾病的关联研究进展

自噬(autophagy)是细胞利用溶酶体降解自身受损的细胞器和大分子物质的过程,在稳定细胞内环境中发挥着重要作用．研究发现,自噬影响血管功能,与血管疾病的病理生理进程密切相关．本文从自噬对血管功能的影响,与血管相关疾病(如动脉粥样硬化、腹主动脉瘤、肺动脉高压、糖尿病血管并发症等)的关系及药物对血管壁细胞自噬的调控进行综述,希望从自噬的角度来了解血管的功能和病变及一些疾病的发生发展进程,为治疗血管相关疾病提供新的思路．